Find an equation for the ellipse that satisfies the given conditions. pre-calc?

Template of the equation is:

(x-g)²/a² + (y-h)²/b² = 1

Center of the ellipse is the midpoint of the minor axis, (g, h) = (0,0)

a² = (length of horizontal axis)²/4

b² = (length of vertical axis)²/4 = (12)²/4 = 36

Distance between the foci = 2√|a²-b²| = 2√|a² - 36| = 14

Note that the distance between the foci is twice the distance from the origin of the ellipse to one focus.

√|a² -36| = 7

a²-36 = 49

a² = 49+36 = 85

Equation of the ellipse:

x²/85 + y²/36 = 1

easy! The foci are located on a vertical line for the time of the beginning place, and (0,0) is the midpoint of the foci, so it incredibly is centrally located and vertically orientated. The x-intercepts often is the covertices (b = 2) and the vertices would be at c^2 = a^2 - b^2 , or 40 9 = a^2 - 4, so a^2 = fifty 3. Your ensuing ellipse is (x^2/4) + (y^2/fifty 3) = a million.

(longest side)^2 = (shortest side)^2 + (foci)^2

only for ellipse

short side=6

foci=14

c^2=14^2 + 6^2

c^2=196+36

c^2=232

c=2sqrt(58)

x=2sqrt(58); y=6,

(x^2/232) + (y^2/36) = 1